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Chapter 4: Problem 8

Fill in each blank with the correct response. $$ -3 x y-2 x y+5 x y= $$

Short Answer

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Step by step solution

01

Identify like terms

Notice that all terms in the expression \( -3xy - 2xy + 5xy \) contain the same variable combination, \(xy\). Therefore, these are like terms and can be combined.
02

Combine like terms

Add the coefficients of the like terms together. The coefficients are \(-3, -2, \) and \(+5\).
03

Perform the addition

Combine the coefficients: \(-3 - 2 + 5 \). Calculate this sum: \(-3 - 2 = -5\) and \(-5 + 5 = 0\).
04

Write the simplified expression

Multiply the combined coefficient by the variable combination: \(0 \times xy = 0 \).

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

coefficients
In algebra, coefficients are the numbers in front of the variables in an expression.
For example, in the term \(-3xy\), \(-3\) is the coefficient.
Coefficients tell you how many of each variable you have.
When combining like terms, you add or subtract their coefficients.
If you see terms like \(-3xy - 2xy + 5xy\), focus on the coefficients: \(-3, -2,\) and \(+5\).
simplifying expressions
Simplifying expressions involves combining like terms to make the expression easier to understand or use.
Like terms have the same variables raised to the same power.
For example, in \(-3xy - 2xy + 5xy\), all the terms have \(xy\).
Combine the coefficients: \(-3 - 2 + 5 = 0\).
The simplified expression, therefore, is just \(0\).
algebraic expressions
An algebraic expression is a combination of variables, numbers, and operations like addition or multiplication.
For example, \(-3xy - 2xy + 5xy\) is an algebraic expression.
The goal in solving algebraic expressions often involves simplifying them.
First, identify like terms.
Then, combine their coefficients.
Lastly, rewrite the expression in its simplest form, which in this case is \(0\).
Remember, algebraic expressions can have more than one variable and different types of terms.

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Most popular questions from this chapter

For each polynomial, first simplify, if possible, and write it in descending powers of the variable. Then give the degree of the resulting polynomial and tell whether it is a monomial, a binomial, \(a\) trinomial, or none of these. $$ 6 p^{5}+4 p^{3}-8 p^{5}+10 p^{2} $$

Our system of numeration is called a decimal system. In a whole number such as 2846 each digit is understood to represent the number of powers of 10 for its place value. The 2 represents two thousands \(\left(2 \times 10^{3}\right),\) the 8 represents eight hundreds \(\left(8 \times 10^{2}\right),\) the 4 represents four tens \(\left(4 \times 10^{1}\right),\) and the 6 represents six ones (or units) \(\left(6 \times 10^{\circ}\right)\) \(2846=\left(2 \times 10^{3}\right)+\left(8 \times 10^{2}\right)+\left(4 \times 10^{1}\right)+\left(6 \times 10^{0}\right) \quad\) Expanded form $$ \text {Keeping this information in mind,} $$ Divide 2846 by \(2,\) using paper-and-pencil methods: \(2 \longdiv { 2 8 4 6 }\)

Evaluate. $$ 277 \div 1000 $$

A computer can perform \(466,000,000\) calculations per second. How many calculations can it perform per minute? Per hour?

Decide whether each expression is equal to \(0,1,\) or \(-1 .\) $$ -(-13)^{0} $$
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